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Submission #498652

# Submission time Handle Problem Language Result Execution time Memory
498652 2021-12-26T04:44:05 Z model_code NoM (RMI21_nom) C++17
52 / 100
 500 ms 59676 KB 
// nom_naive_optimized_popovici.cpp
#include <iostream>
#include <fstream>
#include <algorithm>
 
/*
     Time       O(M * N ^ 2)
     Memory     O(M * N)
*/
 
 
constexpr int MOD = (int)1e9 + 7;
constexpr int MAXN = 3000;
constexpr int MAXM = 3000;
 
int dp[MAXM + 1][MAXN + 1];
 
int comb[2 * MAXN + 1][2 * MAXN + 1];
int pow2[2 * MAXN + 1], fact[2 * MAXN + 1];
int counter[MAXM];
 
inline void add(int& x, int y) {
    x += y;
    if (x >= MOD)
        x -= MOD;
}
 
void prec(int N, int M) {
    for (int i = 0; i <= 2 * N; i++) {
        comb[i][0] = 1;
        for (int j = 1; j <= i; j++) {
            add(comb[i][j], comb[i - 1][j]);
            add(comb[i][j], comb[i - 1][j - 1]);
        }
    }
 
    for (int i = 0; i < 2 * N; i++) {
        counter[i % M]++;
    }
 
    pow2[0] = fact[0] = 1;
    for (int i = 1; i <= 2 * N; i++) {
        pow2[i] = (2LL * pow2[i - 1]) % MOD;
        fact[i] = (1LL * i * fact[i - 1]) % MOD;
    }
}
 
 
 
int main() {
    std::istream& fin = std::cin;
    std::ostream& fout = std::cout;
 
    int N, M;
    fin >> N >> M;
 
    prec(N, M);
    
    dp[M][N] = 1;
    int used = 0;
 
    for (int rem = M; rem > 0; rem--) {
        used += counter[rem];
        for (int pairs = 0; pairs <= N; pairs++) {
            if (dp[rem][pairs] == 0) 
                continue;
 
            int need = counter[rem - 1];
            for (int p = 0; p <= pairs; p++) {
                int others = 2 * N - 2 * pairs - used;
 
                if (need > p + others || need < p)
                    continue;
 
                int current = (1LL * comb[pairs][p] * comb[others][need - p]) % MOD;
                // current = (1LL * current * pow2[p]) % MOD;
                current = (1LL * current * dp[rem][pairs]) % MOD;
                add(dp[rem - 1][pairs - p], current);
            }
        }
    }
 
    int answer = (1LL * dp[0][0] * pow2[N]) % MOD;
    for (int rem = 0; rem < M; rem++) {
        answer = (1LL * answer * fact[counter[rem]]) % MOD;
    }
 
    fout << answer << "\n";
 
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 0 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 0 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 992 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 0 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 992 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 7 ms 4056 KB Output is correct
23 Correct 2 ms 2764 KB Output is correct
24 Correct 4 ms 3916 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 3 ms 2896 KB Output is correct
27 Correct 5 ms 4684 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 0 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 992 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 7 ms 4056 KB Output is correct
23 Correct 2 ms 2764 KB Output is correct
24 Correct 4 ms 3916 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 3 ms 2896 KB Output is correct
27 Correct 5 ms 4684 KB Output is correct
28 Correct 7 ms 8396 KB Output is correct
29 Correct 23 ms 10436 KB Output is correct
30 Correct 30 ms 11476 KB Output is correct
31 Correct 7 ms 8692 KB Output is correct
32 Correct 31 ms 11064 KB Output is correct
33 Correct 54 ms 13044 KB Output is correct
34 Correct 71 ms 18280 KB Output is correct

Subtask #5
0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 0 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 1356 KB Output is correct
12 Correct 1 ms 1100 KB Output is correct
13 Correct 1 ms 844 KB Output is correct
14 Correct 1 ms 972 KB Output is correct
15 Correct 1 ms 1100 KB Output is correct
16 Correct 1 ms 1100 KB Output is correct
17 Correct 1 ms 972 KB Output is correct
18 Correct 1 ms 1100 KB Output is correct
19 Correct 1 ms 992 KB Output is correct
20 Correct 2 ms 1868 KB Output is correct
21 Correct 2 ms 1996 KB Output is correct
22 Correct 7 ms 4056 KB Output is correct
23 Correct 2 ms 2764 KB Output is correct
24 Correct 4 ms 3916 KB Output is correct
25 Correct 4 ms 3916 KB Output is correct
26 Correct 3 ms 2896 KB Output is correct
27 Correct 5 ms 4684 KB Output is correct
28 Correct 7 ms 8396 KB Output is correct
29 Correct 23 ms 10436 KB Output is correct
30 Correct 30 ms 11476 KB Output is correct
31 Correct 7 ms 8692 KB Output is correct
32 Correct 31 ms 11064 KB Output is correct
33 Correct 54 ms 13044 KB Output is correct
34 Correct 71 ms 18280 KB Output is correct
35 Correct 51 ms 34212 KB Output is correct
36 Correct 471 ms 49272 KB Output is correct
37 Correct 41 ms 33468 KB Output is correct
38 Correct 200 ms 39532 KB Output is correct
39 Correct 356 ms 41016 KB Output is correct
40 Execution timed out 657 ms 59676 KB Time limit exceeded